Entries from various style manuals edit

Merriam-Webster’s Standard American Style Manual (1985)

. . . many editors prefer to use en dashes because of the visual clarity they provide and because of the distinction they make between en dashes used to mean “to” and hyphens used to connect elements in compound words. (En dash, at 15.)
Publishers make various use of the en dash, and no one set of rules can be said to be standard. Some common uses of the en dash include using it as a replacement for the hyphen following the prefix that is added to an open compound, as a replacement for the word to between capitalized names, and to indicate linkages, such as boundaries, treaties, or oppositions.
pre–Civil War architecture
the New York–Connecticut area
Chicago–Memphis train
Washington–Memphis train
the Dempsey–Tunney fight
(En Dash, at 16.)

Merriam-Webster’s Manual for Writers & Editors (1998)

Style manuals have historically been written by editors working for particular publications or publishing houses, and have described the particular style rules they follow, usually taking unequivocal stands on issues about which there is in fact considerable diversity of opinion. By contrast, this manual—like the Merriam-Webster dictionaries—attempts to reflect the actual practice of American writers and editors. Its first edition was perhaps the first commercial attempt to develop a major style manual by means of the methods of descriptive lexicography that are the hallmark of this company’s dictionaries. (preface)
The en dash replaces a hyphen in compound adjectives when at least one of the elements is a two-word compound. It replaces the word to between capitalized names, and is used to indicate linkages such as boundaries, treaties, and oppositions.
post–Cold War era
Boston–Washington train
New Jersey–Pennsylvania border
male–female differences or male-female differences

Comment: The tone here is more prescriptive than in the previous edition. It is not clear whether dropping the comma after linkages was an intentional change.

(En Dash and Long Dashes, at 13)

APA Publication Manual, 6th ed. (2010)

. . . used between words of equal weight in a compound adjective (e.g, Chicago–London flight) . . . use no space before or after. (at 4.13, under en dash)

Comment: At least to me, not all of APA’s uses of the en dash are obvious from this cursory treatment. It’s also not necessarily obvious what’s meant by equal weight; would this suggest equal weight in Arab–Israeli conflict but unequal weight in Arab-Israeli spouse? In APA publications, the latter example would presumably never arise, because APA do not use hyphens in open compounds that indicate ethnic identity, even when those compounds are used as adjectives (e.g., Asian American participants [at 3.14]).

The Chicago Manual of Style, 15th ed. (2003)

The en dash is used in place of a hyphen in a compound adjective when one of its elements is an open compound or when two or more of its elements are open compounds or hyphenated compounds. As illustrated by the first four examples below, en dashes separate the main elements of the new compounds more clearly than hyphens would. (“hospital” versus “nursing home”, “post” versus “World War II”, etc.), thus preventing ambiguity.
post–World War II years
a hospital–nursing home connection
a nursing–home care policy
a quasi-public–quasi-judicial body (or, better, a body that is quasi-public and quasi-judicial)
(at 6.85)

The Chicago Manual of Style, 16th ed. (2010)

The en dash can be used in place of a hyphen in a compound adjective when one of its elements consists of an open compound or when both elements consist of hyphenated compounds. This editorial nicety may go unnoticed by the majority of readers; nonetheless, it is intended to signal a more comprehensive link than a hyphen would. It should be used sparingly, and only when a more elegant solution is unavailable. As the first two examples indicate, the distinction is most helpful with proper compounds, whose limits are established within the larger context by capitalization. The relationship in the third example depends to some small degree on an en dash that many readers will perceive as a hyphen connecting music and influenced. The relationships in the fourth example, though also clear enough, are less awkwardly conveyed with a comma.
the post–World War II years
Chuck Berry–style lyrics
country music–influenced lyrics (or lyrics influenced by country music)
a quasi-public–quasi-judicial body (or, better, a quasi-public, quasi-judicial body)
(at 6.80)

Comment: Chicago’s position has clearly evolved since the 13th ed. (which offered no alternative to the last example). Much of the change seems to reflect the belief that most readers will not notice any difference between the en dash and the hyphen. Though the implication is strongly that this use is a last resort, there is the indication that the en dash may, as mentioned in the 15th ed., better convey the distinction better than would a hyphen (e.g., post–World War II is better than post-World War II). There is a potentially significant change from the 15th ed. in compounds for which this use is acceptable: either one open compound or two hyphenated compounds. In 6.78, the 16th ed. gives the example the London–Paris train; presumably from 6.78 and 6.80, Chicago–San Francisco flight would be acceptable, but from 6.80, it would seem that San Francisco–Los Angeles flight would not be. Chicago apparently think the close association provided by hyphens makes it easier to see that the en dash links two compounds; it could be argued, however, that with open compounds, it is easier to see that the linking en dash is not just another hyphen.